AutoD2 {pastecs} | R Documentation

## AutoD2, CrossD2 or CenterD2 analysis of a multiple time-series

### Description

Compute and plot multiple autocorrelation using Mahalanobis generalized distance D2. AutoD2 uses the same multiple time-series. CrossD2 compares two sets of multiple time-series having same size (same number of descriptors). CenterD2 compares subsamples issued from a single multivariate time-series, aiming to detect discontinuities.

### Usage

    AutoD2(series, lags=c(1, nrow(series)/3), step=1, plotit=TRUE,
            add=FALSE, ...)
    CrossD2(series, series2, lags=c(1, nrow(series)/3), step=1,
            plotit=TRUE, add=FALSE, ...)
    CenterD2(series, window=nrow(series)/5, plotit=TRUE, add=FALSE,
            type="l", level=0.05, lhorz=TRUE, lcol=2, llty=2, ...)

### Arguments

`series` | regularized multiple time-series
`series2` | a second set of regularized multiple time-series
`lags` | minimal and maximal lag to use. By default, 1 and a third of the number of observations in the series respectively
`step` | step between successive lags. By default, 1
`window` | the window to use for CenterD2. By default, a fifth of the total number of observations in the series
`plotit` | if `TRUE` then also plot the graph
`add` | if `TRUE` then the graph is added to the current figure
`type` | The type of line to draw in the CenterD2 graph. By default, a line without points
`level` | The significance level to consider in the CenterD2 analysis. By default 5%
`lhorz` | Do we have to plot also the horizontal line representing the significance level on the graph?
`lcol` | The color of the significance level line. By default, color 2 is used
`llty` | The style for the significance level line. By default: `llty=2`, a dashed line is drawn
`...` | additional graph parameters

### Value

An object of class 'D2' which contains:

`lag` | The vector of lags
`D2` | The D2 value for this lag
`call` | The command invoked when this function was called
`data` | The series used
`type` | The type of 'D2' analysis: 'AutoD2', 'CrossD2' or 'CenterD2'
`window` | The size of the window used in the CenterD2 analysis
`level` | The significance level for CenterD2
`chisq` | The chi-square value corresponding to the significance level in the CenterD2 analysis
`units.text` | Time units of the series, nicely formatted for graphs

### WARNING

If data are too heterogeneous, results could be biased (a singularity matrix appears in the calculations).

### Author(s)

Frédéric Ibanez (ibanez@obs-vlfr.fr), Philippe Grosjean (phgrosjean@sciviews.org)

### References

Cooley, W.W. & P.R. Lohnes, 1962. Multivariate procedures for the behavioural sciences. Whiley & sons.

Dagnélie, P., 1975. Analyse statistique à plusieurs variables. Presses Agronomiques de Gembloux.

Ibanez, F., 1975. Contribution à l'analyse mathématique des évènements en écologie planctonique: optimisations méthodologiques; étude expérimentale en continu à petite échelle du plancton côtier. Thèse d'état, Paris VI.

Ibanez, F., 1976. Contribution à l'analyse mathématique des évènements en écologie planctonique. Optimisations méthodologiques. Bull. Inst. Océanogr. Monaco, 72:1-96.

Ibanez, F., 1981. Immediate detection of heterogeneities in continuous multivariate oceanographic recordings. Application to time series analysis of changes in the bay of Villefranche sur mer. Limnol. Oceanogr., 26:336-349.

Ibanez, F., 1991. Treatment of the data deriving from the COST 647 project on coastal benthic ecology: The within-site analysis. In: B. Keegan (ed), Space and time series data analysis in coastal benthic ecology, p 5-43.

### See Also

`mahalanobis`, `acf`

### Examples

    data(marphy)
    marphy.ts <- as.ts(as.matrix(marphy[, 1:3]))
    AutoD2(marphy.ts)
    marphy.ts2 <- as.ts(as.matrix(marphy[, c(1, 4, 3)]))
    CrossD2(marphy.ts, marphy.ts2)
    # This is not identical to:
    CrossD2(marphy.ts2, marphy.ts)
    marphy.d2 <- CenterD2(marphy.ts, window=16)
    lines(c(17, 17), c(-1, 15), col=4, lty=2)
    lines(c(25, 25), c(-1, 15), col=4, lty=2)
    lines(c(30, 30), c(-1, 15), col=4, lty=2)
    lines(c(41, 41), c(-1, 15), col=4, lty=2)
    lines(c(46, 46), c(-1, 15), col=4, lty=2)
    text(c(8.5, 21, 27.5, 35, 43.5, 57), 11, labels=c("Peripheral Zone", "D1",
            "C", "Front", "D2", "Central Zone")) # Labels
    time(marphy.ts)[marphy.d2$D2 > marphy.d2$chisq]

[Package pastecs version 1.3-2 Index]